Question

two vessels containing 104 litres and 91 litres of milk respectively find a measure of a bucket of maximum capacity which can measure the milk of either vessels and exact number of times (Hint find the HCF of 104 and 91)

Answer 1

HCF of 104 and 91 is 13
so ans is a bucket 13 litres
mearures 91 lit= 7 times
measures 104 lit =8 times

Answer 2

Given :

Two vessels containing 104 litres and 91 litres of milk.

To Find:

Find a measure of a bucket of maximum capacity which can measure the milk of either vessels and exact number of times.

Solution:

Here we have to find out capacity of bucket which completely divide the capacity of vessels. Means we have to find out H.C.F of 104 and 91:

H.C.F of 104 and 91 can be find out by prime factorization method:

First find prime factorization of 104:

104 = 2 ×2 ×2 ×13                        ...1)

Now find prime factorization of 91:

91 = 7 ×13                                   ...2)

From equation 1) and equation 2), it is clear that:

H.C.F = 13

Means capacity of vessel is 13 Litres.

104 litres of vessels can measure by bucket in number of times:

$\mathbf{Number\ of\ times= \dfrac{104}{13} =8}$

91 litres of vessels can measure by bucket in number of times:

$\mathbf{Number\ of\ times= \dfrac{91}{13} =7 }$

A bucket of maximum capacity is 13 Litres which can measure the milk of 104 litres and 91 litres vessels in 8 and 7 times respectively.